What this lesson covers
This one takes a single question whose answer trips both rules in a row: 1000/3 is six characters so it cannot go in, its decimal runs on forever so that cannot either, and truncating or rounding at the fourth digit leaves exactly one legal entry. Then the mixed number that quietly changes value: 31/2 is not three and a half, it is fifteen point five.
00:00 The form is part of the answer
00:18 The field
00:42 The method
01:26 The mixed number trap
01:48 Your turn
02:16 Three ways this goes wrong
02:34 Recap
The pump question is original, written for SAT Climb.
Worked examples
The questions the video works, written out: the setup, each step, the answer and the trap.
0:42Example 1
A pump moves 1,000 liters of water in 3 minutes at a constant rate. How many liters does it move per minute? The answer box holds 5 characters (6 if the answer starts with a minus sign), and the fraction bar and the decimal point each cost a character.
- Liters per minute is total liters over minutes: .
- Count the characters in 1000/3: 1, 0, 0, 0, /, 3. That is six. It does not fit in five cells. Rule one: a fraction that does not fit becomes its decimal.
- , which runs on forever. Still too long. Rule two: truncate or round so the decimal fills the box, which here means stopping at the fourth digit.
- Four digits is 333.3. Count it: 3, 3, 3, ., 3 is five characters. It fits. Rounding gives the same string, because the next digit is a 3.
- Check: 333.3 x 3 = 999.9, which is 1000 to the accuracy the box allows.
Answer: 333.3
One answer trips both rules in a row: the exact fraction is too long, so it has to become a decimal, and the decimal never ends, so it has to be cut at the last cell. The near misses all score zero: 1000/3 is six characters, 333 stopped two digits too early, and 333.33 is six characters again. Fill every cell, then stop.
1:26Example 2
Your answer to a grid-in works out to three and a half. What do you type?
- Do not type the mixed number. 31/2 looks like three and a half to you, but the machine reads the digits in order: thirty-one over two, which is 15.5.
- A space will not save it: 3 1/2 is not an accepted form either.
- Convert. As an improper fraction, . As a decimal, 3.5.
- Check: 7 divided by 2 is 3.5, and 3.5 x 2 = 7.
Answer: 7/2 or 3.5
Both entries are three characters and both name the right value. The mixed number is the trap because it does not look wrong on the screen; it quietly changes your answer to 15.5, so right work scores zero.
1:48Example 3
The answer to a grid-in is . Four students type 2/3, .6666, 0.667 and .67. Which one scores zero?
- 2/3 is the exact value, three characters. It scores.
- . The entry .6666 truncates at the fourth digit and fills all five cells. It scores.
- 0.667 rounds at the fourth digit with a leading zero, five cells filled. It scores.
- .67 stopped at the second digit with two cells still empty. A decimal that does not fit has to fill the box, so .67 is rejected, and so are 0.67, .66 and 0.66.
Answer: .67 scores zero
Rounding is allowed, but only at the last cell the box gives you. .67 is the trap because it is how the number is written in every math class; on this test it is not accurate enough. The same rule holds with a minus: for , the entries -1/3, -.3333 and -0.333 are accepted, and -.33 and -0.33 are rejected, because the minus already took one of the six cells.
Lesson transcript
The narration of the video, word for word, under its chapter headings.
The answer box holds five characters. Six if your answer starts with a minus. The fraction bar counts. The decimal point counts. An answer that is too long has to change form. A pump moves one thousand liters in three minutes. Liters per minute is one thousand over three. Count the characters. One, zero, zero, zero, slash, three. That is six. It does not fit. So rule one: a fraction that does not fit becomes its decimal. One thousand divided by three runs on forever. Still too long. Rule two: truncate or round at the fourth digit. Four digits gives you three hundred thirty three point three. Five characters. It fits, and it scores. Now the one that quietly changes your answer. Three and a half. Type three, one, slash, two, and the machine reads thirty one halves. Fifteen point five. Write it as seven over two, or as three point five. Your turn. The answer is two thirds. One of these four scores zero. Ten seconds. Point six seven. Two thirds, point six six six six, and zero point six six seven all pass. Point six seven stopped too early. Three ways this goes wrong. A mixed number with a space in it. Rounding too early, so point six six is rejected. And forgetting that the minus sign takes a character before you have typed a single digit. Get it right. Then get it in.